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I'm currently reading around the topic of quintessence and other models for dark energy and was hoping someone could explain to me what is meant by slow-roll in terms of quintessence and inflation etc. (scalar fields) and is it needed/necessary (is it possible to have a viable scenario compatible with observations with no slow-roll)?

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What is dark energy?

In general relativity, pressure is attractive and tension is repulsive. Pressure has units of energy per volume (more commonly expressed as force per area) and density has units of mass per volume. Since mass = energy in relativity we can equate pressure with density. Dark energy can be thought of as a fluid permeating all of space with a positive density but equal and opposite (negative) pressure. Thus dark energy has an equation of state, or ratio of pressure/density of w=-1. Since tension is repulsive, for w<-1/3 the tension overwhelms the mass and expansion is accelerated. Dark energy is a scalar field as it doesn't have a "direction" (a vector field would give space some sort of "wood-grain" like structure). In quantum field theory, every field is associated with a particle, and scalar fields are associated with zero-spin particles.

But w=-1 is a special case where the word "fluid" is misleading. First of all, the fluid doesn't dilute upon expansion. A piston full of said fluid will experience a negative pressure trying to make it contract. If you force the piston to expand, the energy you put into the piston is used to create more dark energy, keeping the density of the stuff inside the same.

But that's not the only strange thing about w=-1. A swimmer in the ocean (w~1e-15 - 1e-12) or a galaxy "swimming" in the cosmic microwave background (w=1/3) can tell how fast they are moving with respect to the fluid. However, for w=-1 the fluid doesn't provide a reference frame, so it's meaningless to ask "are we moving with respect to dark energy or not?". Thus it's equivalent to say "dark energy" is a vacuum if we take the the word "vacuum" to be the absence of anything that can provide a reference frame, i.e. the absence of any matter or energy that we can "grab on to".

Slow roll inflation

Cosmic inflation was a period of extremly high dark energy density in the early universe (and almost no "ordinary" mass/energy), so high that any normal piece of matter today, or even a neutron star, would be immediately ripped apart by the expansion. But at one point almost all of this got converted into normal mass/energy (dark energy has zero entropy but gases made out of matter or photons have entropy, so the conversion is thermodynamically favored). However, it is not clear whether this process was sudden (like a balloon popping) or gradual (like a stretched spring wearning out). The model of slow roll inflation is the latter, gradual case.

Why do we need the slow roll?

See this question.

Will our present day dark energy go the way of inflation?

During inflation the "dark energy" was basically the only thing around. But we are heading into a similar period as our current dark energy remains at it's tiny buy constant value while everything else slowly decays away into photons and dilutes into nothingness. However, it is possible that the dark energy we have now will also one day be converted into other, as-of-yet unknown particle(s). So little is known about dark energy we can't say for sure what will happen.

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